Direct, Inverse, and Joint Variation Calculator

The calculator will find the constant of variation and other values for direct, inverse (indirect), joint, and combined variation problems, with steps shown.

varies
as the power of of 
as the power of of
as the power of of
Write here the 'find k' condition. For example, write x=3, y=5, z=15, if you are given "z=15, when x=3, y=5".
Write here the 'find variable' condition. For example, write y=2, z=10, if you are given "find x, when y=2, z=10".
If you don't need to find a variable, leave this field empty.

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Solution

Your input: find the constant of variation $$k$$$given $$z=k \frac{x^{2}}{y}$$$, $$z=7$$$when $$x=5$$$ and $$y=3$$$and find $$y$$$ when $$z=12$$$and $$x=1$$$.

We have that $$z=k \frac{x^{2}}{y}$$$. Plug in the given values to find $$k$$$: $$7=k \cdot \frac{5^{2}}{3^{1}}$$$. Solving this equation, we obtain that $$k=\frac{21}{25}$$$.

Now find $$\mathtt{\text{y}}$$$. Plug in the given values and found $$k$$$ to find $$y$$$: $$12=\frac{21 \frac{1^{2}}{y^{1}}}{25}$$$.

From this equation, we have that $$y=\frac{7}{100}$$$. Answer: the constant of variation is $$k=\frac{21}{25}$$$, $$y=\frac{7}{100}$$\$.